One of the buzziest, edgiest shows in London is heading to the West End. Following a seven-week run at the Lyric Hammersmith, Spring Awakening transfers to the Novello theatre on 21 March, joining a growing number of mainstream commercial productions, including Wicked and the soon-to-close Avenue Q, targeted at younger audiences. Those two shows seem somewhat chaste compared with Spring Awakening, which has drawn attention for its scenes of wanking, teenage rebellion and an interval cliffhanger that gives new meaning to the term "dramatic climax".

This in-your-face quality – along with the show's young cast and stripped-back, music-gig vibe – is a large part of the reason why Spring Awakening has drawn favourable comparisons with youth-oriented rock musicals of yore, such as Hair and Rent. Some critics have been less enthusiastic, preferring Frank Wedekind's original 1891 play on which the musical is based.

So what do people the same age as the characters think of the show? Inconveniently lacking teenagers of my own, I collared three undergraduate drama students and set off for the Lyric Hammersmith to find out. My agenda was to get their reaction and speak to as many other young people as possible about the show. I was accompanied in the interviewing process by one of the students, 21-year-old Sarah Butcher, who proved a dab hand with a notepad. Approximately 30–40% of the audience, which was packed out, appeared to be teenagers and early twentysomethings; the Lyric says this percentage is often higher on weeknights.

The show itself is a slowburner: it starts with a thoughtful solo by the female lead, Wendla (Charlotte Wakefield), and builds for about 15 minutes to the first big tear-it-up number, The Bitch of Living, which earned cheers from both young and older audience members. The energy in the auditorium was palpable. Surveying the bar in the interval, I noticed that many young people seemed to be there in groups; one bunch of excitable mid-teenagers said they had come along from their performing arts college in Kingston as it was part of their course, but they chorused that the show was "awesome".

Such high praise continued across the board from the 30 or so teenagers we met. The most consistent sentiment concerned the show's direct relevance to young people's lives: "It's about us – how young people deal with the issues adults don't want to talk to us about," said Katy Reese, a quiet 15-year-old sitting with her mother. "The storyline is really engaging," agreed Tanika Yearwood, a bubbly 16-year-old dressed in black. "They don't hide anything and pretend like we don't know about it or we shouldn't know about it."

Others were at pains to distance this show from what they consider the mainstream of musical theatre: "It's not a 'jazz hands' musical," said Ciara Rogers, 18, who came to the show with her older sister. She went on earnestly: "You might actually listen to the type of music that's on stage." Charlie, an enormously tall 16-year-old, in the company of his younger brother and three family friends from America, was more categorical: "Musicals are not cool. This is not a musical."

While we were speaking, my other two students, Anna Poyhonen and Alisdair Hinton, both 20, were standing to one side and chatting intently. "It's like a darker version of High School Musical," ventured Anna, carefully. "High School Musical is so unashamedly watchable and happy," agreed Alisdair. "That's the world of school we all wish we had. This is more real."

Talking in the bar afterwards, Anna, Alisdair and Sarah agreed that, while they enjoyed the show, the target age was probably about five years younger than them, which suggests Spring Awakening is aimed at audiences who are the same age as the characters.

Perhaps the most distinctive aspect of the show ­– its big "concept" –­ is that while the action takes place in the late 19th century, the musical staging is in a contemporary indie-rock mode; the songs come across as the angry, passionate subtext underlying the characters' repressed, unhappy lives. This device worried some professional critics, but Alisdair felt that keeping Wedekind's original setting of 1891 actually made the musical more relevant: "It would have been the easiest thing in the world to make it be happening now, but the show says that the things you're feeling now were also happening then. Teenagers always say, 'You don't know what this feels like.' But this might make it easier for kids today to watch."

At this point we were distracted by the arrival of Aneurin Barnard, the smokily handsome and seriously talented 21-year-old who plays the leading male character, Melchoir. (Anna had a Winslet-esque 'gather' moment.)

Back to the play. Another problem for some critics was that Spring Awakening softened some of the original play's very hard edges, in particular the rape of Wendla by Melchoir, which is here presented as a tender and consensual (if tentative) act. Although Wendla initiates physical contact with Melchior, she hesitates several times before saying yes to having sex. Sarah suggested that this was a way to make the moment contemporary: "In the original play, her virginity is taken. But this feels like a truer representation. She makes a decision."

Alisdair agrees that the show does "suffer somewhat from being in a post-Skins world": the stickily realistic sex scenes in the E4 series have clearly raised the bar for depictions of intimacy. A scene in which the character Hanschen masturbates received top marks from the group for its messy realism, but the central sex scene was deemed too "sugar-coated". Says Sarah: "We all secretly know the first time is kind of horrific."

A particularly upsetting aspect of the show is the fate of Wendla, who becomes pregnant and dies in a backroom abortion forced upon her by her mother. It was this particular plot point that guided the Lyric's approach to outreach, says James Blackman, co-director of the theatre's lauded creative learning department: "I was concerned that the message of that storyline is that you get pregnant and you're going to die, which was not a message I wanted young women to take away," says Blackman.

The Lyric took this project so seriously that they even produced a short video about sexual and reproductive health, featuring young actors and created with the NHS, the young person's sexual heath charity Brook and the BBC. The DVD is being distributed free of charge to more than 4,000 young people, and is on offer to anyone coming to see the show who asks for it. The show's producers are clearly keen to ensure that teenagers keep booking: when Spring Awakening comes into the West End, a special ticketing scheme will allow 15-19-year-olds to get the best available seats for £20.

Matthew Byam Shaw, producer of the show's West End transfer, is at pains to characterise Spring Awakening as a new kind of family show, rather than one particularly aimed at young people: "I can see parents and grandparents going along with their teenagers," he says. And while the notion of sitting beside one's parents during Spring Awakening's graphic scenes may strike some as excruciating in the extreme, Byam Shaw argues that, on the contrary, one of society's problems is that parents struggle to connect to their adolescent children. "Maybe this show can start some important conversations," he suggests.

On the night we went, that seemed to be borne out. A few parent–child pairings were on display, and 16-year-old Maddie, an American on holiday, told me that when she saw Spring Awakening in New York two years ago, her mother discussed what happens to Wendla with her both before and after the show.

Noble ideas about sex education videos and life lessons aside, the young people I spoke to loved the show because they saw their own experiences reflected in it. Spring Awakening celebrates all the turbulent emotions that teenagers experience, but which are so often demonised – anger, passion, frustration, elation. As 16-year-old Elana Bryan puts it, "We know how they feel."